On quasimultiperfect numbers

P. Anantha Reddy, C. Sunitha and V. Siva Rama Prasad
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 68–73
DOI: 10.7546/nntdm.2020.26.3.68-73
Full paper (PDF, 324 Kb)

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Authors and affiliations

P. Anantha Reddy
Q.Q. Govt. Polytechnic
Chandulalbaradari, Hyderabad, Telangana-500064, India

C. Sunitha
Department of Mathematics and Statistics, RBVRR Womens College
Narayanaguda, Hyderabad, Telangana-500027, India

V. Siva Rama Prasad
Professor(Retired), Department of Mathematics, Osmania University
Hyderabad, Telangana-500007, India

Abstract

For a positive integer n, let σ(n) and ω(n) respectively denote the sum of the positive divisors of n and the number of distinct prime factors of n. A positive integer n is called a quasimultiperfect (QM) number if σ(n) = kn + 1 for some integer k ≥ 2. In this paper we give some necessary conditions to be satisfied by the prime factors of QM number n with ω(n) = 3 and ω(n) = 4. Also we show that no QM n with ω(n) = 4 can be a fourth power of an integer.

Keywords

• Quasimultiperfect number
• Quasitriperfect number

2010 Mathematics Subject Classification

• 11A25

References

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